In Serge Lang's Algebra on page 772 in the middle there is an expression of this form


I don't understand what $Z[A(C)]$ is supposed to mean. Thanks.

  • 1
    $\begingroup$ Please provide more context. Not everyone has his book. $\endgroup$ – Lukas Kofler Sep 11 at 8:58
  • $\begingroup$ You can google a pdf of it. But the C is a K-family and A(C) is a family of objects of C that admit a finite resolution with elements of C. And A is an abelian category. $\endgroup$ – rrr123 Sep 11 at 9:26

The $Z$ denotes the integers, and $[A(C)]$ the set of isomorphism classes of objects in $A(C)$. Then $Z[A(C)]$ is just the free abelian group with generators the elements of $[A(C)]$.


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